Mér finnst líklegt að fundurinn verði stuttur, en það er ólíklegt að við klárum allt í dag.

Because finnast in this kind of sentence works as an impersonal verb meaning to seem or to feel to someone.

• mér is dative and means to me
• finnst is the 3rd person singular form of finnast

So Mér finnst líklegt... is literally something like It seems likely to me...

This is a very common Icelandic pattern for giving an opinion:

• Mér finnst þetta gott = I think this is good / This seems good to me
• Mér finnst líklegt... = I think it is likely...

They are similar, but not identical.

• mér finnst often sounds more like it seems to me or I find
• ég held að is more directly I think that / I believe that

So Mér finnst líklegt að... has a slightly more evaluative, impression-based feel:

• Mér finnst líklegt að... = It seems likely to me that...
• Ég held að... = I think that...

Both are natural, but mér finnst líklegt is especially good when you are judging probability.

Because it is being used predicatively with a whole clause as its content: að fundurinn verði stuttur.

In Icelandic, when an adjective like líklegur, ólíklegur, gott, slæmt, etc. refers to an entire statement or clause, it usually appears in the neuter singular.

So:

• líklegt = likely
• ólíklegt = unlikely

This is similar to English It is likely that... where the adjective describes the whole idea, not a masculine or feminine noun.

Here að introduces a subordinate content clause, similar to English that.

So:

• líklegt að fundurinn verði stuttur = likely that the meeting will be short
• ólíklegt að við klárum allt í dag = unlikely that we finish everything today

In English, that is often optional. In Icelandic, að is much more normally kept in sentences like this.

Because verði is the present subjunctive of verða, while verður is the indicative.

After expressions like:

• líklegt að...
• ólíklegt að...
• mér finnst líklegt að...

Icelandic often uses the subjunctive in the subordinate clause, because the statement is not being presented as a plain fact. It is something probable, possible, doubtful, or judged.

So:

• fundurinn verður stuttur = the meeting will be short
• fundurinn verði stuttur = that the meeting will be short, in a clause governed by likelihood/judgment

Because Icelandic very often uses verða for a future state:

• Fundurinn verður stuttur = The meeting will be short

Even though verða often literally means become, in many everyday future statements it corresponds to English will be.

So in this sentence:

• að fundurinn verði stuttur naturally means that the meeting will be short

If you used sé stuttur, the meaning would lean more toward is short rather than a future prediction.

Because fundurinn means the meeting, while fundur means a meeting.

The ending -inn is the suffixed definite article in Icelandic. Instead of a separate word like English the, Icelandic usually attaches the article to the noun.

So:

• fundur = a meeting
• fundurinn = the meeting

Because fundurinn is the subject of the subordinate clause að fundurinn verði stuttur.

Even though the whole clause comes after að, inside that clause fundurinn is still the thing that will be short, so it stays in the nominative.

A simple way to see it:

• Fundurinn verður stuttur = The meeting will be short

When this becomes a subordinate clause, the subject does not change case:

• að fundurinn verði stuttur

Because stuttur agrees with fundurinn.

fundurinn is:

• masculine
• singular
• nominative

So the adjective must also be:

• masculine
• singular
• nominative

That gives stuttur.

Compare:

• fundurinn er stuttur
• bókin er stutt
• húsið er stutt would be neuter, so stutt

The form of the adjective changes to match the noun it describes.

In það er ólíklegt að..., það is a dummy or anticipatory subject, much like English it in it is unlikely that...

So:

• það er ólíklegt að... = it is unlikely that...

In the first half, Icelandic often simply says:

• Mér finnst líklegt að...

That is a very natural pattern with finnast. The clause after it supplies the content of what seems likely.

You may also hear structures with það in similar contexts, but the version in your sentence is very normal and idiomatic.

Good question. In this sentence, klárum is understood in a subjunctive environment after ólíklegt að, but for 1st person plural many present subjunctive forms look the same as the indicative.

So even though:

• the clause is the kind that often takes the subjunctive
• the form klárum looks just like the ordinary present indicative

This is normal. Icelandic does not always show the subjunctive with a visibly different ending in every person.

So the grammar of the sentence points toward subjunctive usage, even though the form itself does not visibly change here.

Because after að, Icelandic uses subordinate clause word order, where the subject normally comes before the finite verb.

So:

• við klárum allt í dag = main-clause order can already look like this
• after að, this subject-before-verb order is the normal choice

That is why you get:

• að fundurinn verði stuttur
• að við klárum allt í dag

English speakers often expect something closer to main-clause inversion patterns, but Icelandic keeps the subject in front here.

Here allt is the direct object of klárum, so it is in the accusative.

The verb klára means to finish / complete, and it takes an object:

• klára verkefnið = finish the project
• klára allt = finish everything

allt is the neuter singular form of allur used as a pronoun meaning everything.

In the neuter singular, nominative and accusative often look the same, so the form allt does not visibly show the difference, but its role here is object.

Because Icelandic very often uses the present tense for future meaning when the time is clear from context.

So:

• við klárum allt í dag can mean we finish everything today or we will finish everything today

The phrase í dag makes the time frame clear, so there is no need for a separate future tense marker. This is very common in Icelandic.

Likewise, English can sometimes do something similar:

• We finish this today
• We’re meeting tomorrow

But Icelandic relies on this kind of present-for-future usage even more naturally in many cases.